I have a small problem/puzzle to solve which goes as follows:
(I have already calculated it, however I am not sure I followed the right reasoning as mathematics is not my strong point and after building a Java app to brute force it, it crashed on out-of-memory error):

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We have ten bikes (b1, b2, …, b10) that need to be sold at 3 shops
houses (s1, s2, s3). Each shop can sell at most 5 bikes.

How many solutions are possible? You may solve this using
mathematics, or brute force with a spreadsheet, or small program.

This is a problem in combinations where the order of selection does not matter.
Selecting r things from n: nCr = n! / (r! (n-r)!)